Explanation Given: The initial temperature of the room was 70 ° F and the given conditions are B ( 0 ) = 98.6 ° F , B ( T ) = 85 and B ( T + 1 ) = 80 . Calculation: Consider the differential equation. d B d t = k ( B − 70 ) (1) Here, B is the body’s temperature, t is the time elapsed and k is the constant. Separate the variables of Equation (1) and integrate both sides with respect to t . ∫ d B B − 70 = ∫ k d t ln | B − 70 | = k t + C ln | B − 70 | = k t + C | B − 70 | = e C e k t Simplify the above equation. B − 70 = A e k t B = 70 + A e k t (2) Substitute 0 for t and B ( 0 ) = 98.6 in Equation (2). B ( 0 ) = 70 + A e k ( 0 ) 98.6 = 70 + A A = 28.6 Substitute 28.6 for A in Equation (2). B = 70 + 28.6 e k t (3) Substitute B ( T ) = 85 in Equation (3)

6th Edition

ISBN: 9781284127003

Author: ZILL

Publisher: JONES+BARTLETT LEARNING,LLC (CC)

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Chapter 2.7, Problem 19E

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The number of hours elapsed before the body was found.

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The number of hours elapsed before the body was found.

Solution Summary: The author explains how the body was found after 1.6hours.

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Chapter 2 Solutions